Anyway, it seems the PS3 outlasted my LA40A650 which died a little while ago. So off we trotted and managed to snag a new 55" Samsung Series 6 Smart TV (non 4K), model UA55J6200 for $1380 at Harvey Norman at Knox City, Melbourne. The Samsung 55" J6200 is an amazing piece of tech, and we really love it, the LED is so much better than the old LCD we had and the SmartTV features are really neat (it's handy to be able to watch Netflix directly from the TV).
So the UA55J6200 Samsung is all good.....
Lets define "doesn't work". In my setup, the PS3 runs through an Onkyo NR515AE amp, and having the HDMI out from the AVR running to the HDMI 1 port of the Samsung 55" Series J6200 results in no signal being picked up by the TV (but sound coming from the AVR). I knew the PS3 was still working because of the audio output via the AVR and the HDMI display was working because I plugged the AVR HDMI out into an HDMI-enabled DELL monitor, and the display worked too. But, no matter of swapping HDMI cables got it working on the UA55J6200, no joy at all.
So I went trawling the far reaches of the internet looking for help. Apparently people have been having this problem with various TVs for at least 5 years. There are plenty of people wanting to help, but generally none of the answers helped me (and many others).
Amongst the things I diligently tried but didn't work included resetting my PS3 to factory defaults, but it didn't work. I got a non 1080p signal, and when the system switched back to 1080p the TV lost signal. Clearly, whatever that did wasn't the problem. So avoid doing that if you can help it (I lost a lot of game saves, etc. doing that).
Anyway, this post on the Tom's Hardware forums by Sarahqt was on the money.
I'm going to be lazy and quote the post here, verbatim:
To fix it you need to head to Display Settings where in you can find an option called "Deep color Output (HDMI)". Turn this option from automatic to OFF and viola! the 1080p output from the PS3 works just fine again! I think the problem definitely lies with the PS3- software/hardware I cant tell.
So, on the PS3 do:
SETTINGS>DISPLAY SETTINGS >DEEP COLOR OUTPUT (HDMI) > OFF
(default is Auto, which doesn't work on the Samsung 55" Series 6 6200).
I hope this helps someone else. I found this as frustrating as hell, but now it's working just fine.